Description of this paper

Below are two topics, labelled A and B, which will be the subject of this assignment. Thequestions that you need to answer are listed after the topics, and are labelled 1-3. Notethat you will need to refer to both of topics A and B in answering Question 1, but notethat you only need to actually collect data and analyse it for one of the topics (A or B)to answer Questions 2 and 3.

A. Take a random sample of 30 words from a large dictionary, and test whether or notyou know each word, according to the instructions on the following page.(I) What proportion of words in the dictionary do you know?(II) Is there evidence that you know more than half of the words in the dictionary?

B. Time how long (in seconds) it takes you to sprint the distance between wickets ona cricket pitch (which is 20.12 metres), from a running start. Do this eight times.David also did this, and managed the following times, in seconds:2.6 2.7 2.7 2.7 2.6 2.5 2.7 2.8Compare these data to your own times.(I) Is there evidence that you are faster than David, i.e. your average time isshorter?(II) How much shorter (or longer) is your average sprint time than David?s average?

The questions you need to answer in your assignment submission are given below.

1. For both of the topics labelled A and B above, identify the appropriate methods ofinference to answer each of the research questions labelled (I) and (II).(You do not need to include your reasoning ? all we are after here is the answer.)

2. Choose one of the two topics labelled A or B above that is of particular interest toyou, and collect data as described. Use Excel or R to analyse the data, includingin your answer:

(a) The raw data. (If choosing to do B, record your time to one decimal place.)

(b) Appropriate numerical and graphical summaries of the data.

(c) A 95% confidence interval for the key parameter of interest.

(d) An appropriate hypothesis test.Make sure you include in your answer the null and alternative hypotheses, andthe correct P-value to three decimal places (calculated using the computer).

(e) A relevant conclusion that makes use of the above results.

3. What assumptions were required in order to complete Questions 2c and 2d? Werethese assumptions reasonable? Include details of any necessary assumptionchecks.

Additional Instructions

Note that you may collect data in groups ? this might make the job a bit easier for you!

A. ? This test works well if you have a helper to find and test you on the randomwords.

? It?s best to use a large dictionary which tells you how many words are definedin it ? then you could also estimate how many words you know! (Can you workout how?)

?The library contains many such dictionaries. I recommend the Macquarie (asit contains Australian jargon), although you are welcome to use a non-Englishlanguage dictionary if you like...

? It is actually quite difficult to generate a simple random sample of words fromthe dictionary. Here is a recommended method for doing it:

? Work out how many pages are in the dictionary (2198, say).

? Flick through a few pages to get a sense for the maximum number of wordsthat appear on a single page, then choose a number just larger than this(60, say).

? Use a computer to generate a set of maybe 50 pairs of random numbers

?one for page number, one for word number on the page. For example, ona new Excel spreadsheet, you could type =RAND()*2198 in cell A1, then=RAND()*60 in cell A2, then copy this formula down to row 50, and roundup to the next integer. The random number pair (1032, 41) means testyourself on the 41st word on page 1032.

? Each pair of random numbers gives you a potential word to test yourselfon

? but only if there is a word in the dictionary corresponding to therandom page and word numbers. For example, if page 1032 only has 39words on it, then you cannot use the random number pair (1032, 41) toselect a word. Because you may not find a word for every pair of randomnumbers, you need to generate more than 30 pairs of random numbers, toensure that you can test yourself on exactly 30 words.

? When assessing whether or not you know a word, see if you can use it in asentence which illustrates its meaning. If the word has multiple meanings,being able to demonstrate knowledge of one of them is good enough!

B. This is easier to do if you have someone timing you. Have a few practice sprintsbefore you start timing, as you may get faster after warming up.